As shoshz said “I think for me just knowing that Dovid haMelech went through so much and left this for us to turn to when we are in trouble or just to feel inspired.”
I remember learning in 12th grade (we had a class and teacher for Tehillim, best class ever!) that Dovid, as the king, encompasses all of klal yisroel. Therefore, everyone relates to Tehillim regardless of what s/he is going through at that point as it was written through David. There is also an interesting medrash about David’s eyes were all different colors…can’t remember it or how it fit in to this though…anyone know what I’m talking about?